Sound · decibel arithmetic
Decibel calculator: add and subtract dB.
Decibels are logarithmic, so you cannot add them like ordinary numbers. Enter several levels to get the combined level, or subtract the background noise from a reading to find the level of the source alone.
Inputs
Result
Enter at least one level to see the total.
How decibels add and subtract
Decibels are a logarithmic scale, so two sources cannot be added as plain numbers. Sound levels from uncorrelated sources combine by adding their power, then converting back to dB: total = 10 x log10 (10^(L1/10) + 10^(L2/10) + ...). Sengpielaudio gives the same rule: for incoherent sources "their combined effect is the sum of their acoustic power". Two equal sources therefore add about 3 dB, and four equal sources add 6 dB.
Worked example, adding. Three machines at 85 dB, 85 dB and 80 dB: the total is 88.6 dB, only 3.6 dB above the loudest. Four identical 60 dB sources give 66 dB, which matches Sengpielaudio's own motorcycle example (60 dB + 10 log 4 = 66 dB).
Worked example, subtracting. A reading of 72 dB with the source on and 66 dB with it off. The power difference is 10^7.2 - 10^6.6, which converts back to 70.7 dB for the source alone: a correction of 1.3 dB. Subtraction is the same power arithmetic run backwards; it is derived from the addition rule above.
Two limits matter. The addition rule assumes the sources are uncorrelated (a violin and a trumpet, not the same signal sent to two speakers). And when the gap between total and background is small, subtraction gets unreliable: treat a gap under about 3 dB as a rule of thumb, not a published standard, and re-measure.
Frequently asked questions
What is 80 dB plus 80 dB?
83 dB. Doubling the number of equal sources adds about 3 dB, not 80.
Why can I not just add decibels?
Decibels are ten times the base-10 logarithm of a power ratio. Sources add in power, so you convert each level to power, add, and convert back.
Does this work for two speakers playing the same signal?
No. This is for uncorrelated (incoherent) sources. Identical signals from two speakers can add more or less than this depending on phase and position.
How do I remove background noise from a measurement?
Measure the total with the source on, then the background with it off, and enter both under Subtract background noise. If the two are within about 3 dB, re-measure in a quieter setting.
Sources
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Scope
Sound-level arithmetic only. It does not weight frequencies, so enter all levels in the same weighting (all dBA or all dB SPL). For a noise exposure assessment use a calibrated meter.